Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}3x+2y &= 4 \\ -8x+2y &= 2\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-1$ and the bottom equation by $1$ $\begin{align*}-3x-2y &= -4\\ -8x+2y &= 2\end{align*}$ Add the top and bottom equations. $-11x = -2$ Divide both sides by $-11$ and reduce as necessary. $x = \dfrac{2}{11}$ Substitute $\dfrac{2}{11}$ for $x$ in the top equation. $3( \dfrac{2}{11})+2y = 4$ $\dfrac{6}{11}+2y = 4$ $2y = \dfrac{38}{11}$ $y = \dfrac{19}{11}$ The solution is $\enspace x = \dfrac{2}{11}, \enspace y = \dfrac{19}{11}$.